Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class FunkyNumbers {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int a,b,num2,flag=0;
		double c1,c2,coef;
		Scanner scan = new Scanner(System.in);
		int num = scan.nextInt();
		num2=num*2;
		for(a=1;a<=Math.sqrt(num2);a++) {
			coef = -num2 + a*a + a;
			c1=(-1+Math.sqrt(1-4*coef))/2;
			c2=(-1-Math.sqrt(1-4*coef))/2;
			if(((int)c1==c1 && c1>0 )|| ((int)c2==c2 && c2>0)) {
				System.out.println("YES");
				//System.out.println(c1 + " "+c2 + " "+a);

				flag = 1;
			}
			if(flag==1)break;
		}
		
		if(flag!=1) {
			System.out.println("NO");
		}
		System.out.println();
	}

}